(d^4x)/(dt^4)-x=0

Lösung

\frac{d ^{4} x}{d t ^{4}} - x = 0

x = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t)

Schritte zur Lösung

\frac{d ^{4} x}{d t ^{4}} - x = 0

Solve linear ODE:

x = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t)

x = c_{1} e^{t} + c_{2} e^{- t} + c_{3} cos (t) + c_{4} sin (t)

y^{^{''''}} - 44 y^{^{'''}} + 484 y^{^{''}} = 0

y^{^{'''}} + 4 y^{^{''}} - 128 y = 0, y (0) = e^{4 x}

y^{^{''}} + 2 y^{^{'}} + 24 y = 0

y^{^{''}} - 9 y^{^{'}} + 5 y = 0

2 y^{^{''}} - 2 y^{^{'}} + y = 0, y (0) = - 1, y^{^{'}} (0) = 0